Question

A toroid of mean radius $16\text{cm}$ has $1000$ turns of wire closely wounded on a ferromagnetic core of relative permeability $400$. What is the magnetic induction $B$ within the core for a magnetizing current of $1\text{A}$ ?

• A. $0.00125\text{T}$
• B. $0.00250\text{T}$
• C. $1\text{T}$
• D. $0.5\text{T}$

Answer 1

The correct option is D $0.5\text{T}$

Given:
$r=16\text{cm}=16\times {10}^{-2}\text{m};N=1000$
${\mu }_r=400;i=1\text{A}$

So, magnetic field inside the core of toroid is given by

$B=\frac{{\mu }_0{\mu }_{r}Ni}{2\pi r}$

$B=\frac{4\pi \times {10}^{-7}\times 400\times 1000\times 1}{2\pi \times 16\times {10}^{-2}}$

$\therefore B=0.5\text{T}$

Hence, option $\left(d\right)$ is correct.